Newton迭代法收敛性

The Convergence of the Newton Iteration

给出一种新的,具有较大收敛域的Newton迭代法和Newton下山法收敛性定理,以及误差估计式.它不要求函数f(x)存在二阶导数,只需要函数f(x)存在一阶导数,便可根据文中定理对其收敛性进行判别,弥补了以往相关定理的不足,并通过数值例子给予验证.

In this paper, some new theorems of convergence of the Newton iteration and Newton descent method in larger convergence domain are introduced, and the expressions of error estimate about these two iterations are presented. It is required that there only exist one order derivate but not two order derivate for the function f（x） to discriminate the convergence of the Newton iteration in the theorem. The rushs are tested and verified by the numerical examples.